Given an algebraically closed field $\mathbb F$ and its prime field $\mathbb Q$, what would be the degree of extension $[\mathbb F:\mathbb Q]$? Is it always infinite? It for sure is for $[\mathbb C:\mathbb Q]$ since the latter is countable and the former is uncountable.
2026-04-09 15:16:41.1775747801
Degree of extension of a prime field $\mathbb Q$ to an algebraically closed field $\mathbb F$
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